2.1 problem 1

Internal problem ID [11]

Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 1.3. Slope fields and solution curves. Page 26
Problem number: 1.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_linear, class A]]

Solve \begin {gather*} \boxed {y^{\prime }+\sin \relax (x )+y=0} \end {gather*}

Solution by Maple

Time used: 0.016 (sec). Leaf size: 19

dsolve(diff(y(x),x) = -sin(x)-y(x),y(x), singsol=all)
 

\[ y \relax (x ) = \frac {\cos \relax (x )}{2}-\frac {\sin \relax (x )}{2}+{\mathrm e}^{-x} c_{1} \]

Solution by Mathematica

Time used: 0.057 (sec). Leaf size: 25

DSolve[y'[x]== -Sin[x]-y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{2} \left (-\sin (x)+\cos (x)+2 c_1 e^{-x}\right ) \\ \end{align*}